Given y = $ae^{bx+5}$ Differentiating with y with respect to x, ⇒ $\frac{dy}{dx}$ = $ae^{bx+5}$ × b ⇒ $\frac{dy}{dx}$ = by ... (i) (Since y = $ae^{bx+5}$) Diffrentiating (i) with respect to x, ⇒ $\frac{d^2y}{dx^2}$ = b $\frac{dy}{dx}$ ⇒ $\frac{d^2y}{dx^2}$ = $\left( \frac{1}{y} \frac{dy}{dx} \right) \frac{dy}{dx}$ ... from (i) ⇒ y $\frac{d^2y}{dx^2}$ = $\left( \frac{dy}{dx} \right)^2$